Activation Energy

FIELDS OF STUDY: Physical Chemistry; Inorganic Chemistry; Biochemistry

ABSTRACT

The activation energy of a process is defined, and its importance in chemical processes is elaborated. Activation energy is a widely variable quantity in different reactions but is nevertheless characteristic of any specific reaction process.

Activation Energy in Chemical Reactions

Activation energy can be thought of as a barrier that the reactants in a chemical reaction must overcome if the reaction is to proceed to the formation of products. The molecules that are involved must rearrange to form either a transition state or an intermediate that is higher in energy than the starting materials. An intermediate is a stable chemical structure formed during a reaction process that can often be captured and isolated by chemical means. Once this structure is formed, the reaction process can either progress to form products or revert back to the original reactants.

Activation energy is the energy required for a specific chemical reaction to occur. In a reaction, two reactant molecules contact each other with the energy of their ambient states. (The ambient state of a material can be thought of as its "default" state—the state it takes at one atmosphere of pressure and what is commonly considered to be room temperature.) In the case of a spontaneous reaction, the energy of the collision is sufficient to initiate the formation of the transition state or intermediate. In a nonspontaneous reaction, the energy of the molecular collision is not sufficient, and the two molecules will not interact. The input of some additional energy is required to drive the two molecules together so that the transition state or intermediate is formed and the reaction can proceed. The energy released in the transformation of reactants into products is generally sufficient to drive the reactions of other molecules in the reaction mixture.

Another way to look at activation energy is to think of it as the minimum amount of energy that two interacting molecules must gain in order to weaken bonds between atoms in both molecules so that those bonds can be rearranged. Since chemical reactions are essentially processes of breaking and making bonds, having sufficient energy to overcome the strength of the appropriate bonds is essential if there is to be any reaction between the two molecules.

Activation Energy and Reaction Rates

Reaction rates can be related directly to their activation energies. This relationship is defined by the Arrhenius equation, formulated in 1884 by the Swedish scientist Svante Arrhenius (1859–1927), who received the Nobel Prize in Chemistry in 1903. The Arrhenius equation relates the rate constant of a reaction to its activation energy and the absolute temperature and has the form

k = Ae⁻E^/RT

where k is the rate constant for the reaction or process; A is the pre-exponential factor, also known in some cases as the frequency factor; E (or E_a) is the activation energy for the reaction or process; R is the gas constant; T is the absolute temperature; and the mathematical constant e is the base of the natural logarithm, so that the natural logarithm (ln) of e is equal to 1. The Arrhenius equation has been found to apply not only to chemical reactions but to physical processes as well. The relationship can be most clearly seen by plotting experimentally determined logarithmic values of k against the inverse of the absolute temperature, 1/T. This results in a straight line plot, from which the activation energy of the reaction or process can be calculated.

The pre-exponential factor A is identified as the value that the specific rate constant k would have if the activation energy E were zero (a spontaneous reaction). In that special case, the exponent −E/RT would also be equal to zero, making e−E/RT equal 1 and thus causing the value of k to be equal to A. For different specific reactions, the value of A ranges over several orders of magnitude, but the rate constant k is determined almost solely by the value of e−E/RT, which can range over several hundred orders of magnitude, depending on the relative values of E and T.

The course of a reaction depends on the relative difference between the energy of the reactants and that of the products. The greater this difference is, the more impetus there is for the reaction to proceed to the formation of products. This is typically illustrated in a plot of energy versus the reaction coordinate, a symbolic representation of the progress of a reaction. In the plot, the energy level of the reactants, on the left, is either higher or lower than that of the products, on the right. In between, a curved line rises from the energy level of the reactants to a maximum value before falling to the energy level of the products. The difference between the energy level of the reactants and this peak energy value represents the activation energy for the reaction, while the difference between the energy levels of the reactants and the products represents the energy released in the reaction, also called its enthalpy.

The specific rate of any individual reaction is determined by its activation energy. However, in mass quantities, the energy differences between reactants and products in the system also play a role. This can be understood by considering the Boltzmann fraction e−E/RT, which describes the fraction of molecules in the system having energy greater than E. As energy is released from several reactions, the fraction of molecules present at any given time with sufficient energy to react increases, and more reactions can occur in any given time period. Each reaction requires the same activation energy, and the amount of energy that is available in the system to permit reactions to occur may be anything from "barely enough" to "excessive."

The activation energy of a reaction can be greatly reduced by the inclusion of a catalyst, a material that takes part in the reaction mechanism but is not consumed in the reaction. Catalysts function by forming an activated complex with the reactants, typically constraining the reactant molecules in an orientation that they would otherwise have to achieve through collision with each other. This reduces the energy necessary to achieve that particular orientation—that is, the activation energy—so that the reaction can proceed. When the reactant molecules are constrained in the activated complex with the catalyst, bonds between certain atoms are weakened and the orientations of atomic and molecular orbitals that must interact are often brought into the proper alignment, or trajectory, for the new bonds to form between atoms.

Activation Energy in Action

The activation energy of a reaction can range from exceedingly small to very large. Two examples serve to illustrate this point. For the first, consider the addition of two parts hydrogen gas (H₂) to one part oxygen gas (O₂). This is an explosive mixture of gases, yet the two mixed gases are quite happy to coexist quietly in the same container, no matter how much is present. The introduction of an initiator such as an electrical spark, however, results in an almost instantaneous reaction to form water (H₂O), accompanied by the release of a great deal of energy. The activation energy of the reaction between hydrogen and oxygen is very low, and the amount of energy released by one reaction is more than sufficient to drive many instances of the reaction in the gas mixture, with each subsequent occurrence releasing an equal amount of energy as the enthalpy of reaction.

The second example is the so-called thermite reaction, in which iron oxide and aluminum metal react to produce aluminum oxide and iron metal. This is a spectacular reaction often demonstrated for chemistry exhibitions. Because the activation energy of the thermite reaction is very high, the reaction is very difficult to initiate and must typically be ignited by a burning piece of magnesium metal; once it has begun, however, it is essentially impossible to stop it due to the amount of energy that is released. Typically, the iron metal falls out of the reaction mixture as a white-hot liquid.

Activation Energy in Biological Systems

Activation energy applies to biochemical processes as well as to physical processes. The chirping of crickets, for example, is dependent on temperature in a manner that is in complete accord with the Arrhenius equation. In biological systems, the activation energy of processes is made a great deal lower by the catalytic action of protein molecules called enzymes. Enzymes have well-defined three-dimensional structural shapes that allow them to coordinate with other molecules in specific ways, rather like the way a key works with a lock. The coordination normally alters the three-dimensional shape of the substrate molecule or otherwise interacts with it so that specific bonds are weakened and the molecular geometry is changed such that reaction is highly favored.

PRINCIPAL TERMS

• Arrhenius equation: a mathematical function that relates the rate of a reaction to the energy required to initiate the reaction and the absolute temperature at which it is carried out.
• catalyst: a chemical species that initiates or speeds up a chemical reaction but is not itself consumed in the reaction.
• chemical reaction: a process in which the molecules of two or more chemical species interact with each other in a way that causes the electrons in the bonds between atoms to be rearranged, resulting in changes to the chemical identities of the materials.
• reaction rate: how much of a particular reaction or reaction step occurs per unit time.
• transition state: an unstable structure formed during a chemical reaction at the peak of its potential energy that cannot be isolated and ultimately breaks down, either forming the products of the reaction or reverting back to the original reactants.

Bibliography

Arnaut, Luís, Sebastião Formosinho, and Hugh Burrows. Chemical Kinetics: From Molecular Structure to Chemical Reactivity. Oxford: Elsevier, 2007. Print.

Bell, Jerry A. Chemistry: A Project of the American Chemical Society. New York: Freeman, 2005. Print.

Lafferty, Peter, and Julian Rowe, eds. The Hutchinson Dictionary of Science. 2nd ed. Oxford: Helicon, 1998. Print.

Masterton, William L., Cecile N. Hurley, and Edward Neth. Chemistry: Principles and Reactions. 7th ed. Belmont: Brooks, 2012. Print.

Raymond, Kenneth W. General, Organic, and Biological Chemistry: An Integrated Approach. 4th ed. Hoboken: Wiley, 2014. Print.

Zumdahl, Steven S., and Susan Zumdahl. Chemistry. 9th ed. Belmont: Brooks, 2013. Print.